A simplified all-frequency stable formulation with an implicit Coulomb gauge
A potential-based finite element formulation has been developed in the past to circumvent the low-frequency breakdown issues commonly encountered in electromagnetic (EM) simulations of low-frequency and multiscale problems. In this formulation, the magnetic vector and electric scalar potentials have been employed to express the electric field and magnetic flux, leading to a set of two equations that represents all four Maxwell’s equations and the current continuity equation. To enforce the Coulomb gauge, an auxiliary potential has been introduced, which results in a total of three equations to be solved simultaneously. To reduce the number of equations and unknowns needed in a simulation, a simplified formulation is proposed in this paper to enforce the Coulomb gauge implicitly without the need for the auxiliary potential. A numerical example is given to demonstrate the accuracy of the proposed formulation.